Existence of η-Quotients For Squarefree Levels

2019/10/31 by Michael P. Allen, Allen, Michael
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1911.00096

openalex publication_date 2019/10/31 · openalex created_date 2022/07/22 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate which modular form spaces can contain η-quotients, functions of the form f(τ) = ∏_{δ| N} η(δτ)^r_δ. For k≥ 2 even and N coprime to 6, we give necessary conditions for the space M_k(Γ₁(N)) to contain η-quotients. We then show that these conditions are sufficient as well for a large family of squarefree levels N coprime to 6.

Related

• Generating spaces of modular forms with η-quotients
• Proceedings Paper for REU Project Involving Counting Eta-Quotients
• Dimension formulas for modular form spaces of rational weights, the classification of eta-quotient characters and an extension of Martin's theorem
• Theta Products and Eta Quotients of Level 24 and Weight 2
• Some applications of eta-quotients